{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2011:JIOR3ZQBF4ZGDLL3DPYT4RMLVP","short_pith_number":"pith:JIOR3ZQB","schema_version":"1.0","canonical_sha256":"4a1d1de6012f3261ad7b1bf13e458babdee683e244c5cb421284df9d9afca4fe","source":{"kind":"arxiv","id":"1109.6138","version":1},"attestation_state":"computed","paper":{"title":"Biharmonic submanifolds with parallel mean curvature in $\\mathbb{S}^n\\times\\mathbb{R}$","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.DG","authors_text":"Cezar Oniciuc, Dorel Fetcu, Harold Rosenberg","submitted_at":"2011-09-28T09:22:14Z","abstract_excerpt":"We find a Simons type formula for submanifolds with parallel mean curvature vector (pmc submanifolds) in product spaces $M^n(c)\\times\\mathbb{R}$, where $M^n(c)$ is a space form with constant sectional curvature $c$, and then we use it to prove a gap theorem for the mean curvature of certain complete proper-biharmonic pmc submanifolds, and classify proper-biharmonic pmc surfaces in $\\mathbb{S}^n(c)\\times\\mathbb{R}$."},"verification_status":{"content_addressed":true,"pith_receipt":true,"author_attested":false,"weak_author_claims":0,"strong_author_claims":0,"externally_anchored":false,"storage_verified":false,"citation_signatures":0,"replication_records":0,"graph_snapshot":true,"references_resolved":false,"formal_links_present":false},"canonical_record":{"source":{"id":"1109.6138","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DG","submitted_at":"2011-09-28T09:22:14Z","cross_cats_sorted":[],"title_canon_sha256":"8ac08aaf4cc257a8fbc3140db1a80ee5007c9ecaa18ac7d237a78ade1e32487e","abstract_canon_sha256":"bf0bf547214249d6aac15fdac9e5b8a7f4e8c3af770c1654a0ad1047cf44e3e6"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T04:12:09.668783Z","signature_b64":"NynJuwRS7slTXSTrVLMlo1O34PCK0dKLNZhE0vjL2Wg9IoFZYkXlcv5q5Va+g0J3ANn9ziYUvqTe2dIACHOsDg==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"4a1d1de6012f3261ad7b1bf13e458babdee683e244c5cb421284df9d9afca4fe","last_reissued_at":"2026-05-18T04:12:09.668292Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T04:12:09.668292Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Biharmonic submanifolds with parallel mean curvature in $\\mathbb{S}^n\\times\\mathbb{R}$","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.DG","authors_text":"Cezar Oniciuc, Dorel Fetcu, Harold Rosenberg","submitted_at":"2011-09-28T09:22:14Z","abstract_excerpt":"We find a Simons type formula for submanifolds with parallel mean curvature vector (pmc submanifolds) in product spaces $M^n(c)\\times\\mathbb{R}$, where $M^n(c)$ is a space form with constant sectional curvature $c$, and then we use it to prove a gap theorem for the mean curvature of certain complete proper-biharmonic pmc submanifolds, and classify proper-biharmonic pmc surfaces in $\\mathbb{S}^n(c)\\times\\mathbb{R}$."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1109.6138","kind":"arxiv","version":1},"verdict":{"id":null,"model_set":{},"created_at":null,"strongest_claim":"","one_line_summary":"","pipeline_version":null,"weakest_assumption":"","pith_extraction_headline":""},"references":{"count":0,"sample":[],"resolved_work":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57","internal_anchors":0},"formal_canon":{"evidence_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"author_claims":{"count":0,"strong_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"builder_version":"pith-number-builder-2026-05-17-v1"},"aliases":[{"alias_kind":"arxiv","alias_value":"1109.6138","created_at":"2026-05-18T04:12:09.668377+00:00"},{"alias_kind":"arxiv_version","alias_value":"1109.6138v1","created_at":"2026-05-18T04:12:09.668377+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1109.6138","created_at":"2026-05-18T04:12:09.668377+00:00"},{"alias_kind":"pith_short_12","alias_value":"JIOR3ZQBF4ZG","created_at":"2026-05-18T12:26:32.869790+00:00"},{"alias_kind":"pith_short_16","alias_value":"JIOR3ZQBF4ZGDLL3","created_at":"2026-05-18T12:26:32.869790+00:00"},{"alias_kind":"pith_short_8","alias_value":"JIOR3ZQB","created_at":"2026-05-18T12:26:32.869790+00:00"}],"events":[],"event_summary":{},"paper_claims":[],"inbound_citations":{"count":0,"internal_anchor_count":0,"sample":[]},"formal_canon":{"evidence_count":0,"sample":[],"anchors":[]},"links":{"html":"https://pith.science/pith/JIOR3ZQBF4ZGDLL3DPYT4RMLVP","json":"https://pith.science/pith/JIOR3ZQBF4ZGDLL3DPYT4RMLVP.json","graph_json":"https://pith.science/api/pith-number/JIOR3ZQBF4ZGDLL3DPYT4RMLVP/graph.json","events_json":"https://pith.science/api/pith-number/JIOR3ZQBF4ZGDLL3DPYT4RMLVP/events.json","paper":"https://pith.science/paper/JIOR3ZQB"},"agent_actions":{"view_html":"https://pith.science/pith/JIOR3ZQBF4ZGDLL3DPYT4RMLVP","download_json":"https://pith.science/pith/JIOR3ZQBF4ZGDLL3DPYT4RMLVP.json","view_paper":"https://pith.science/paper/JIOR3ZQB","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1109.6138&json=true","fetch_graph":"https://pith.science/api/pith-number/JIOR3ZQBF4ZGDLL3DPYT4RMLVP/graph.json","fetch_events":"https://pith.science/api/pith-number/JIOR3ZQBF4ZGDLL3DPYT4RMLVP/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/JIOR3ZQBF4ZGDLL3DPYT4RMLVP/action/timestamp_anchor","attest_storage":"https://pith.science/pith/JIOR3ZQBF4ZGDLL3DPYT4RMLVP/action/storage_attestation","attest_author":"https://pith.science/pith/JIOR3ZQBF4ZGDLL3DPYT4RMLVP/action/author_attestation","sign_citation":"https://pith.science/pith/JIOR3ZQBF4ZGDLL3DPYT4RMLVP/action/citation_signature","submit_replication":"https://pith.science/pith/JIOR3ZQBF4ZGDLL3DPYT4RMLVP/action/replication_record"}},"created_at":"2026-05-18T04:12:09.668377+00:00","updated_at":"2026-05-18T04:12:09.668377+00:00"}